Alg2 Radical Functions Jeapordy

Simpifying and Operations with Radicals

100

Simplify.

Cube Rt -81p²q¹²

-3q⁴ Cube Rt 3p²

200

sq rt 98x⁴y² - 3x²y sq rt 2

4x²y sq rt 2

300

A rectangle has a width of (4 - sq rt 6) and a length of (7 sq rt 6 + sq rt 3).  Find the area and perimeter of the rectangle

Area: 25 sq rt 6 + 4 sq rt 3 - 42 - 3 sq rt 2

Perimeter: 8 + 12 sq rt 6 + 2 sq rt 3

400

Double Jeopardy 

4th rt 8a³b * 4th rt  10a²b⁷

Or 

Divide 3 + sq rt 7  by 

         2 + 2 sq rt 7

What is 2ab² 4th rt 5a

What is ...    2 + sq rt 7   

                        6

500

(10 + 3 sq rt 7) (10 + 3 sq rt 7) 

Or

((Sq Rt 50 - 2  Sq Rt 8)(Sq Rt 2 + 3))

What is 37?

What is 2 + 3 Sq Rt 2

Rational Exponents

100

Write the expression in exponent form

Cube Rt 9x⁷y⁴

What is ...(9x⁷y⁴)^1/3

Or 9x^7/3y^4/3

200

Write the expression in exponential form.

4th Rt (-2a)⁵

(-2a)^5/4

300

Simplify the Expression with Rational Exponents

p^1/4 * p ^3/2

or 

(8x²)^2/3

p^1/4 * p^6/4

Add Exponents p ^7/4

What is..... p 4th Rt p³

8^2/3x^4/3  = Cube Rt 64x⁴ = 

What is ... 4x³ cube rt x

400

Use exponent rules to simplify. Write all answers in simplest radical form

(54^1/2)^5/3

(54)^1/2

(54)^5/6

(54)^3/6

(54)^1/3 = Cube Root 54 = 

Cube Rt 27 * Cube Rt 2

What is 3 Cube Rt 2

500

4th Root of 16x²y⁶ * Sq Rt 28x¹⁰y²²

(4²x²y⁶)^1/4 * (2²7x¹⁰y²²)^1/2

4^1/2x^1/2y^{3/2 *} 2 7^1/2x⁵y¹¹

2y x^1/2y^{1/2 *} 2 7^1/2x⁵y¹¹

4x⁵y¹² Sq Root 7xy

Solving Radical Equations

100

Solve Each Equation. Check for extraneous solutions

Sq root (3x - 2)    + 4 = 11

Sq root (3x - 2)   = 7

(Sq root (3x - 2))²   = 7²

3x - 2 = 49         3x = 51    x = 17                 Check  sq rt 3* 17 - 2   + 4   = 11

sq rt 51 - 2 = 7  Yes sq rt 49 = 7 

200

Solve Each Equation. Check for extraneous solutions

Sq rt of (x - 5) = x - 11

(Sq rt of (x - 5))² = (x - 11)²

x - 5 = x² - 22x + 121

x² - 23x + 126 = (x - 14)(x - 9) .... x = 14   

chk sq rt (14 -5)  = (14 - 11)²    9 = 9 Yes 

chk sq rt 9 - 5 Does Not =  9 - 11 .... 4 Not = -2      

300

Solve Each Equation. Check for extraneous solutions

Cube Rt 9x + 45 = 3 

9x + 45 = 27

9x = 27 - 45

9x = - 18    ..... What is x = -2

ck Cube Root 9(-2) + 45 = 3...cube rt 27=3  

What is 3 = 3

400

Solve Each Equation. Check for extraneous solutions

(45 - 2x)^1/2 = (a - 6)^1/2

45 - 2x = x - 6

- 3x = -51   What is x = 17

check:  Sq Rt 45 - 2(17)  = sq rt 17 - 6

           sq rt 11 = sq rt 11

500

Solve Each Equation. Check for extraneous solutions

(q - 21)^1/2 = (q)^1/2 + 7

((q - 21)^1/2 )²= ((q)^1/2 + 7)²

q - 21 = q + 14(q)^1/2 + 49

- 70 = 14 sq rt q .... (-5)² = (sq rt q)²   25 = q 

chk: Sq rt 25 - 21 = sq rt 25 + 7 ... 

2 Does Not = 12    NO SOLUTION 

Translations & Graphing Radical Functions

100

The square root parent function is translated so that it has an endpoint of (-4, 1), then vertically compressed by a factor of 1/3.Write an equation that could represent this function. 

f(x) = 1/3 sq root (x - 4)    - 1

200

The cubic parent function is reflected over the x axis, vertically compressed by a factor of 1/3  then shifted so that it's turning point is located at (-6,-2). Write an equation that represents this new function. 

Describe ALL transformations 

f(x) = - 1/3 cube root x + 6    -  2

reflected over x axis, 

compressed by a factor of 1/3, 

left 6, and 

down 2. 

300

Graph the function below and identify its key charactoristics.  f(x) = - Sq Rt x + 4  + 2

D: _____  R:______  Endpoint/Turning pt: ____

As x ->  ______ f(x) -> ______ 

As x ->  ______ f(x) -> ______

sq root fn flipped over at (-4, 2)

D: x > -4  R: y < 2 

Endpoint/Turning pt: (-4, 2)

As x ->  infinity f(x) -> negative infinity

As x ->  -4  f(x) -> 2

400

Double Jeopardy: Graph the function and identify its key charactoristics.   f(x) = 2 Cube Rt x - 3  - 1

D: _____  R:______  Endpoint/Turning pt: ____

As x ->  ______ f(x) -> ______ 

As x ->  ______ f(x) -> ______

D: |R  R:  |R   Endpoint/Turning pt: (3, -1)

As x ->  Infinity f(x) -> Infinity

As x ->  neg infinity f(x) -> neg infinity

500

Graph the function and identify its key charactoristics.   f(x) = - 3/4 Cube Rt x + 1

D: _____  R:______  Endpoint/Turning pt: ____

As x ->  ______ f(x) -> ______ 

As x ->  ______ f(x) -> ______

D: |R  R:  |R   Endpoint/Turning pt: (-1, 0)

As x ->  Infinity f(x) -> negative Infinity

As x ->  negative infinity f(x) -> positive infinity

Find Inverse Fns & verify inverse relationships

100

Write the inverse of the function below. 

 f(x) = Sq Root x - 5 

Inverse function : f^-1 (x) =

x = sq root y - 5

(x + 5)² = (sq root y)²

x² + 10x + 25 = y

f^-1(x) = x² + 10x + 25

200

Write the inverse of the function below. Graph both functions to verify the relationship. 

 f(x) = -2/3x - 4 

Inverse function : f^-1 (x) =

x = -2/3y - 4 ........   x + 4 = -2/3y 

-3/2(x + 4) = y

Inverse function : f^-1 (x) = -3/2x - 6

Graph y = x ----,  graph (0, -4) slope -2/3 and

graph (0, -6) slope - 3/2 

300

Determine whether the pair of functions are inverse.

f(x) = 6x - 15   g(x) = 1/6x + 5/2 

f(g(x)) = 6(1/6x + 5/2)  - 15

            = x + 15 - 15 ....               f(g(x)) = x

g(f(x)) = 1/6 (6x -15)  + 5/2 

= x - 15/6 + 5/2 .... x - 5/2 + 5/2 ...g(f(x)) = x 

Yes f(g(x) = x and g(f(x)) = x Inverse Fns!!!

400

Determine whether the pair of functions are inverse.

f(x) = 1/4 x³ - 3 and g(x) = Cube Rt 4x -12 

f(g(x)) = 1/4 ((4x -12)^1/3)³ - 3

f(g(x)) =1/4 (4x - 12) - 3

f(g(x)) = x - 3 - 3 

f(g(x)) = x - 6 

NOT INVERSES

500

Solve the Equation. Check

Sq Rt 6x + 19  - 4 = x

Sq Rt 6x + 19   = x + 4

(Sq Rt 6x + 19)²   = (x + 4)²

6x + 19 = x² + 8x + 16... 0 = x² + 2x - 3            (x + 3 )(x - 1)

Check Sq Rt 6(-3) + 19 - 4 =-3,  -3 = -3 check  Check Sq rt 6(1) + 19 - 4 = 1  sq rt 25 - 4 = 1        1 = 1 CHECK